Define and solve a problem by using Solver

Solver is a Microsoft Excel add-in program you can use for what-if analysis. Use Solver to find an optimal (maximum or minimum) value for a formula in one cell — called the objective cell — subject to constraints, or limits, on the values of other formula cells on a worksheet. Solver works with a group of cells, called decision variables or simply variable cells that are used in computing the formulas in the objective and constraint cells. Solver adjusts the values in the decision variable cells to satisfy the limits on constraint cells and produce the result you want for the objective cell.

Put simply, you can use Solver to determine the maximum or minimum value of one cell by changing other cells. For example, you can change the amount of your projected advertising budget and see the effect on your projected profit amount.

Note Versions of Solver prior to Excel 2007 referred to the objective cell as the "target cell," and the decision variable cells as "changing cells" or "adjustable cells". Many improvements were made to the Solver add-in for Excel 2010, so if you're using Excel 2007 your experience will be slightly different.

In the following example, the level of advertising in each quarter affects the number of units sold, indirectly determining the amount of sales revenue, the associated expenses, and the profit. Solver can change the quarterly budgets for advertising (decision variable cells B5:C5), up to a total budget constraint of $20,000 (cell F5), until the total profit (objective cell F7) reaches the maximum possible amount. The values in the variable cells are used to calculate the profit for each quarter, so they are related to the formula objective cell F7, =SUM (Q1 Profit:Q2 Profit).

In the Set Objective box, enter a cell reference or name for the objective cell. The objective cell must contain a formula.

Do one of the following:

If you want the value of the objective cell to be as large as possible, click Max.

If you want the value of the objective cell to be as small as possible, click Min.

If you want the objective cell to be a certain value, click Value of, and then type the value in the box.

In the By Changing Variable Cells box, enter a name or reference for each decision variable cell range. Separate the non-adjacent references with commas. The variable cells must be related directly or indirectly to the objective cell. You can specify up to 200 variable cells.

In the Subject to the Constraints box, enter any constraints that you want to apply by doing the following:

In the Solver Parameters dialog box, click Add.

In the Cell Reference box, enter the cell reference or name of the cell range for which you want to constrain the value.

Click the relationship ( <=, =, >=, int, bin, or dif ) that you want between the referenced cell and the constraint.If you click int, integer appears in the Constraint box. If you click bin, binary appears in the Constraint box. If you click dif, alldifferent appears in the Constraint box.

If you choose <=, =, or >= for the relationship in the Constraint box, type a number, a cell reference or name, or a formula.

Do one of the following:

To accept the constraint and add another, click Add.

To accept the constraint and return to the Solver Parameters dialog box, click OK.Note You can apply the int, bin, and dif relationships only in constraints on decision variable cells.

You can change or delete an existing constraint by doing the following:

In the Solver Parameters dialog box, click the constraint that you want to change or delete.

Click Change and then make your changes, or click Delete.

Click Solve and do one of the following:

To keep the solution values on the worksheet, in the Solver Results dialog box, click Keep Solver Solution.

To restore the original values before you clicked Solve, click Restore Original Values.

You can interrupt the solution process by pressing Esc. Excel recalculates the worksheet with the last values that are found for the decision variable cells.

To create a report that is based on your solution after Solver finds a solution, you can click a report type in the Reports box and then click OK. The report is created on a new worksheet in your workbook. If Solver doesn't find a solution, only certain reports or no reports are available.

To save your decision variable cell values as a scenario that you can display later, click Save Scenario in the Solver Results dialog box, and then type a name for the scenario in the Scenario Name box.

When you save a model, enter the reference for the first cell of a vertical range of empty cells in which you want to place the problem model. When you load a model, enter the reference for the entire range of cells that contains the problem model.

Tip You can save the last selections in the Solver Parameters dialog box with a worksheet by saving the workbook. Each worksheet in a workbook may have its own Solver selections, and all of them are saved. You can also define more than one problem for a worksheet by clicking Load/Save to save problems individually.